The situation your are in is undeniably unfortunate "if" you are the original purchaser of these camcorders but have no way of proving it, this through having made the transaction by cash but having lost the receipts whereby no other proof of purchase existed like a c/card receipt.
However the reason JVC operates this policy is because they wanted to avoid the situation where dealers would buy up defective camcorders at knock down prices, get them repaired for free, and then resell making the proverbial quick buck!
There is a possibility that this policy could also have been adopted due to pressure from Sony, as it was they who supplied the defective modules and likewise are compensating JVC for the repair costs, something which must be quite a substantial figure as many hundreds of camcorders are affected.
The other unfortunate aspect of all this is that its only people fortunate enough to have web access that would get to know about the "free" repair offer and take advantage of it, as this manufacturing defect has been given super-low profile publicity, and there has to be many camcorder owners without web access totally unaware of the offer and likewise paying out good money for the repair.